Diffusion of finite-size particles in confined geometries

TL;DR

This paper derives a nonlinear diffusion equation for finite-size particles in confined geometries, capturing effects of exclusion and confinement, and compares theoretical predictions with stochastic simulations, with applications to ratchet-driven transport.

Contribution

It introduces a new nonlinear diffusion model that accounts for finite particle size and confinement effects, bridging between single-file and unconfined diffusion regimes.

Findings

The nonlinear diffusion equation accurately predicts particle behavior under various confinement conditions.

Numerical solutions match stochastic particle system simulations.

Excluded-volume and confinement effects significantly alter transport properties in ratchet potentials.

Abstract

The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear diffusion equation for the one-particle probability density function, with an overall collective diffusion which depends on both the excluded-volume and the narrow confinement. By including both these effects the equation is able to interpolate between severe confinement (for example, single-file diffusion) and unconfined diffusion. Numerical solutions of both the effective nonlinear diffusion equation and the stochastic particle system are presented and compared. As an application, the case of diffusion under a ratchet potential is considered, and the change in transport properties due to excluded-volume and confinement effects is examined.